Pith Number

pith:4QRAH6NI

pith:1998:4QRAH6NIO35K6QNK4WVL5JY3MT

not attested not anchored not stored refs pending

The Fluctuation Theorem as a Gibbs Property

Christian Maes

arxiv:math-ph/9812015 v1 · 1998-12-18 · math-ph · math.DS · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4QRAH6NIO35K6QNK4WVL5JY3MT}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T01:38:30.659026Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e42203f9a876faaf41aae5aabea71b64dc0686f72951ef5b9426853f38fe56dd

Aliases

arxiv: math-ph/9812015 · arxiv_version: math-ph/9812015v1 · doi: 10.48550/arxiv.math-ph/9812015 · pith_short_12: 4QRAH6NIO35K · pith_short_16: 4QRAH6NIO35K6QNK · pith_short_8: 4QRAH6NI

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4QRAH6NIO35K6QNK4WVL5JY3MT \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: e42203f9a876faaf41aae5aabea71b64dc0686f72951ef5b9426853f38fe56dd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a1a6fdc5198e6ce44a5213ce087cd8a5080eb53cdaac5688b4fef9f1c35c251e",
    "cross_cats_sorted": [
      "math.DS",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "1998-12-18T15:59:58Z",
    "title_canon_sha256": "c881d9369f10a81ac4a9f5a748bef78f6485aa0319e984f01f3bf1bb5706d00b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/9812015",
    "kind": "arxiv",
    "version": 1
  }
}